\magnification=\magstep1
\noindent
{\it Andrew Marzo}
\bigskip
Your response to the essay question on the midterm
is very good.
You have definitely ``hit all of the high points''
and provided just the right level of detail about
the way the different historians we discussed would
interpret ``quadratic algebra'' problems such as
the one on the YBC 6967 tablet.  The only substantive
comment I have is that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources like this.  So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.
\vfill
\eject
\noindent
{\it Catherine Caracciolo}
\bigskip
You have a very good response to the essay question on the midterm.
You have definitely ``hit all of the high points''
and provided the right level of detail about
the way the different historians we discussed would
interpret ``quadratic algebra'' problems such as
the one on the YBC 6967 tablet.

\bigskip
The substantive
comments I have are first that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources like this.  The
problem is one of solving an equation however
you slice it.   So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.

\bigskip
Next, it would be better to qualify some of the statements
such as:  ``Neugebauer is the only one'' who would
agree with the quote.  He is the only historian {\it we
discussed} who would do so.  But his viewpoint
was actually very influential because
he and his co-workers were the first to translate
and analyze these tablets (also the first to
recognize that they were, in fact, records of
mathematical calculations, and not just record-keeping).
His interpretation was the first one to appear and it
set the tone for scholarship about Old Babylonian
mathematics for many years.

\bigskip
Finally, it is not really correct to say that Neugebauer's
and Hoyrup's interpretations are not supported elsewhere.
There are many examples of problems similar to the one
on YBC 6967 that are known, and Neugebauer and Hoyrup
have published interpretations of them along the
same lines.  Plimpton 322 can be taken as evidence
that the Babylonians knew ``something close to''
the Pythagorean theorem, but there are other interpretations
of that tablet too.

\vfill
\eject
\noindent
{\it Dan Finn}
\bigskip
You have a very good response to the essay question on the midterm.
You have definitely ``hit all of the high points''
and provided just the right level of detail about
the way the different historians we discussed would
interpret ``quadratic algebra'' problems such as
the one on the YBC 6967 tablet.  The only substantive
comment I have is that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources for problems like this.  So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.
\vfill
\eject
\noindent
{\it Sarah Cahn}
\bigskip
You have a very good response to the essay question on the midterm.
You have definitely ``hit all of the high points''
and provided just the right level of detail about
the way the different historians we discussed would
interpret ``quadratic algebra'' problems such as
the one on the YBC 6967 tablet.  The only substantive
comment I have is that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources for problems like this.  So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.

\bigskip
Also, instead of saying ``Neugebauer would solve the problem
this way'' or ``Hoyrup would solve the problem that way''
you really mean to say that they are claiming {\it the 
ancient Babylonians} would have thought about the 
solution of the problem in those terms.  Don't forget
that all of these methods are correct {\it and essentially
equivalent}  from the point of view of modern mathematics.
\vfill
\eject
\noindent
{\it Kyle Kadlick}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only 
thing I would have liked to see in addition was a bit 
more about the connection between the identity
$$(a+b)^2 = (a - b)^2 + 4ab$$
and the actual solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  What is the connection 
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  

Also, there is a bit more behind Rudman's reasons
for rejecting Hoyrup's ``cut and paste'' visualization
than just that his proposed diagram ``looked better.''
I think if you look back it his reasoning you will
see that he thought Hoyrup's way of seeing this
was essentially ``too clever'' to be the basis of 
a general method for solving these problems.
That's questionable, of course.  But it goes
a little deeper than you are indicating.
\vfill\eject
\noindent
{\it Tom Santa Maria}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only
thing I would have liked to see in addition was a bit
more about the actual mathematics.  First, the key identity
that comes into play in these problems can be stated as
$$(a+b)^2 = (a - b)^2 + 4ab.$$
I was also looking for the connection between this and
the actual solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  That is, what is the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  

The other substantive
comment I have is that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources for problems like this.  So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.
\vfill
\eject
\noindent
{\it Astrid Ludwig}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only
thing I would have liked to see in addition was a bit
more about the connection between the identity
$$(a+b)^2 = (a - b)^2 + 4ab$$
and the actual solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  What is the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  
\vfill
\eject
\noindent
{\it Peter Zona}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only
thing I would have liked to see in addition was a bit
more about the actual mathematics.  First, the key identity
that comes into play in these problems can be stated as
$$(a+b)^2 = (a - b)^2 + 4ab.$$
I was also looking for the connection between this and
the actual solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  That is, what is the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  
\vfill
\eject
\noindent
{\it Xuan Ha Nghiem}
\bigskip
Your response to the essay question on the midterm
is very good.
You have definitely ``hit all of the high points''
and provided just the right level of detail about
the way the different historians we discussed would
interpret ``quadratic algebra'' problems such as
the one on the YBC 6967 tablet.  The only substantive
comment I have is that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources like this.  So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.
\vfill\eject
\noindent
{\it Kylee Sullivan}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only
thing I would have liked to see in addition was a bit
more about the connection between the identity
$$(a+b)^2 = (a - b)^2 + 4ab$$
and the actual solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  What is the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  
\vfill
\eject
\noindent
{\it Lucia Bostrom}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well, except
for the ``cut and paste geometry'' interpretation of 
the YBC 6967 tablet offered by Jens Hoyrup.  This similar
to Rudman's ideas in that it gives a proposed geometric 
visualization of the steps in the Babylonian solution
of the YBC 6967 problem.  But it is also different because
the geometric connection is a different one.  That is 
the main additional thing I was looking for here.  

\bigskip
It is good, though, that you explained about the exact
connection between the identity
$$(a+b)^2 = (a - b)^2 + 4ab$$
and the solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet by giving the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams). 
\vfill
\eject
\noindent
{\it Matt Kasuba}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only
thing I would have liked to see in addition was a bit
more about the actual mathematics.  First, the key identity
that comes into play in these problems can be stated as
$$(a+b)^2 = (a - b)^2 + 4ab.$$
I was also looking for the connection between this and
the actual solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  That is, what is the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  

The other substantive
comment I have is that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources for problems like this.  So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.
\vfill
\eject
\noindent
{\it Muhammad Javaid}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only
thing I would have liked to see in addition was a bit
more about the actual mathematics.  
I was also looking for the connection between this and
the actual solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  That is, what is the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  

The ``with geometry in the background'' is a good way of
putting the ideas that Hoyrup and Rudman have about
these examples of Babylonian mathematics.  They 
certainly accept that there is some algebra involved,
since the problem is one of solving an algebraic
equation.  But they would say that the method of
solution shows that the Babylonians were thinking
in geometric terms in one way or another.
\vfill
\eject
\noindent
{\it John Macomber}
\bigskip
Your response to the essay question on the midterm
is very good.
You have definitely ``hit all of the high points''
and provided just the right level of detail about
the way the different historians we discussed would
interpret ``quadratic algebra'' problems such as
the one on the YBC 6967 tablet.  The only substantive
comment I have is that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources for problems like this.  So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.
\vfill
\eject
\noindent
{\it Kevin Sutman}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only
thing I would have liked to see in addition was a bit
more about the actual mathematics.  First, the key identity
that comes into play in these problems can be stated as
$$(a+b)^2 = (a - b)^2 + 4ab.$$
I was also looking for the connection between this and
the solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  That is, what is the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  
\vfill
\eject
\noindent
{\it Max Pettinelli}
\bigskip
This is a good response to the essay question on the midterm.
You have hit most of the important points well.  The only
thing I would have liked to see in addition was a bit
more about the actual mathematics.  First, the key identity
that comes into play in these problems can be stated as
$$(a+b)^2 = (a - b)^2 + 4ab.$$
I was also looking for the connection between this and
the solution of the equation $x^2 - 7x - 60 = 0$
from the YBC 6967 tablet.  That is, what is the connection
between the $x$ here and the $a,b$ in the identity
(or in the geometric diagrams)?  

The other substantive
comment I have is that even people in the
``geometry camp'' (like Hoyrup and Rudman) would
acknowledge that there is {\it some} element of algebra
content in Babylonian sources for problems like this.  So the
picture is a bit less ``black and white'' than you
are making it.  Neugebauer might say there is only
algebra going on here.  But Hoyrup and Rudman would
say that there is a geometric motivation behind the
method of solution of the algebra question.

\bye